MATH327 - Player Unknown’s Battleground: Solo Rating Linear Analysis
Noah B Johnson, Mohammed Al Jardat, Collin Carpenter
11/13/2017
## Warning in strptime(x, format, tz = tz): unknown timezone 'zone/tz/2018g.
## 1.0/zoneinfo/America/Chicago'In the videogame Player Unkown’s Battleground, players compete in a free for all battle arena that takes the form of a pair of islands surrounded by a vast ocean. Players are scattered throughout the island and must search the various buildings and facilities on the islands for weapons and gear that can be used to help survive the battle. Each player will have a rating based upon how well they do in a vareity of different aspects. The purpose of our analysis is to determine if there is a statistical correlation we can draw from this player data that will help us determine what seperates the different players in terms of solo rating.
Normalization of the data
We normalized the data to [0,1] range and plotted the normalized values against the original values to double check that normalization worked
Check the Distribution of each variable
Distribution of each variable with log transformation
vars: 2, 3, 4, & 7 appear to be normally distributed when log transformed
# There are 0.0000 values in ~200 cells of the 90000 element normalmatrix. Loss of data deemed acceptable.
Distribution of each variable with square root transformation
Vars: 5 & 6 look more normally distributed with square root transformation
Histograms of transformed variables
Summary of Multiple Regression for non-transformed variables
##
## Call:
## lm(formula = solo_Rating ~ solo_WinRatio + solo_KillDeathRatio +
## solo_RoundsPlayed + solo_MoveDistancePg + solo_DamagePg +
## solo_KillsPg + solo_AvgSurvivalTime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.09796 -0.10428 -0.00523 0.10475 0.49474
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.137655 0.006220 22.132 < 2e-16 ***
## solo_WinRatio 0.008555 0.021635 0.395 0.69255
## solo_KillDeathRatio -0.216838 0.077880 -2.784 0.00538 **
## solo_RoundsPlayed 1.633815 0.021805 74.930 < 2e-16 ***
## solo_MoveDistancePg 0.385274 0.019078 20.195 < 2e-16 ***
## solo_DamagePg 1.633649 0.108786 15.017 < 2e-16 ***
## solo_KillsPg -1.629142 0.129539 -12.576 < 2e-16 ***
## solo_AvgSurvivalTime -0.007080 0.016339 -0.433 0.66480
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.146 on 9992 degrees of freedom
## Multiple R-squared: 0.3997, Adjusted R-squared: 0.3992
## F-statistic: 950.3 on 7 and 9992 DF, p-value: < 2.2e-16First order model does not look very promising with an adjusted R-squared value of .3992. Future transformations will hopefully increase this value.
Correlation Matrix for non-transformed variables
## track var1 var2 var3 var4
## track 1.00000000 -0.0951925063 -0.06005138 -0.08659303 -0.0312682
## var1 -0.09519251 1.0000000000 -0.05658658 -0.07756071 0.5793137
## var2 -0.06005138 -0.0565865825 1.00000000 0.72561229 -0.1977646
## var3 -0.08659303 -0.0775607132 0.72561229 1.00000000 -0.2259784
## var4 -0.03126820 0.5793136992 -0.19776461 -0.22597835 1.0000000
## var5 -0.11741882 0.1261006396 0.37229531 0.35989254 -0.1607233
## var6 -0.11004922 -0.0469249397 0.63340017 0.88466753 -0.2457212
## var7 -0.09956666 -0.0773213629 0.65628540 0.90537805 -0.2562709
## var8 -0.08238990 -0.0004090853 0.45492268 0.43391719 -0.2418726
## var5 var6 var7 var8
## track -0.1174188 -0.11004922 -0.09956666 -0.0823899021
## var1 0.1261006 -0.04692494 -0.07732136 -0.0004090853
## var2 0.3722953 0.63340017 0.65628540 0.4549226795
## var3 0.3598925 0.88466753 0.90537805 0.4339171887
## var4 -0.1607233 -0.24572117 -0.25627093 -0.2418725737
## var5 1.0000000 0.39692699 0.38475078 0.6791649776
## var6 0.3969270 1.00000000 0.98402862 0.4571464487
## var7 0.3847508 0.98402862 1.00000000 0.4546263913
## var8 0.6791650 0.45714645 0.45462639 1.0000000000Scatter plot of solo_Rating vs each non-transformed variable
Summary of Multiple Regression for transformed variables
##
## Call:
## lm(formula = solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_KillDeathRatio.nrm +
## Log.solo_RoundsPlayed.nrm + Sqrt.solo_MoveDistancePg.nrm +
## Sqrt.solo_DamagePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49657 -0.05850 -0.00151 0.06496 0.30382
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.977309 0.054415 17.960 <2e-16 ***
## Log.solo_WinRatio.nrm 0.029172 0.002346 12.437 <2e-16 ***
## Log.solo_KillDeathRatio.nrm 0.038378 0.016327 2.351 0.0188 *
## Log.solo_RoundsPlayed.nrm 0.154270 0.001602 96.316 <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm 0.455743 0.017438 26.135 <2e-16 ***
## Sqrt.solo_DamagePg.nrm -0.114415 0.066115 -1.731 0.0836 .
## Log.solo_KillsPg.nrm 0.039482 0.016480 2.396 0.0166 *
## solo_AvgSurvivalTime.nrm 0.136473 0.013821 9.874 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09482 on 6938 degrees of freedom
## Multiple R-squared: 0.6692, Adjusted R-squared: 0.6689
## F-statistic: 2005 on 7 and 6938 DF, p-value: < 2.2e-16After several transofrmations on the predictors, our Adjusted R-squared is now sitting at a relatively pleasing .6689. Even further manipulation of the data may allow us to tweek this value a bit.
Dropping the least significant variable transmatrix Sqrt.solo_DamagePg.nrm.
Correlation Matrix for transformed variables
## tracktrans solo_rating.mtrx solo_WinRatio.mtrx
## tracktrans 1.000000000 -0.08887507 -0.0893966
## solo_rating.mtrx -0.088875073 1.00000000 -0.3274858
## solo_WinRatio.mtrx -0.089396598 -0.32748579 1.0000000
## solo_KillDeathRatio.mtrx -0.127687085 -0.22022057 0.7825900
## solo_RoundsPlayed.mtrx -0.001660295 0.69172864 -0.7711185
## solo_MoveDistancePg.mtrx -0.140201211 0.10881856 0.4806081
## solo_DamagePg.mtrx -0.137925165 -0.16434659 0.7108651
## solo_KillsPg.mtrx -0.134591260 -0.18225228 0.7298163
## solo_AvgSurvivalTime.mtrx -0.098855539 -0.04991211 0.5417566
## solo_KillDeathRatio.mtrx solo_RoundsPlayed.mtrx
## tracktrans -0.1276871 -0.001660295
## solo_rating.mtrx -0.2202206 0.691728639
## solo_WinRatio.mtrx 0.7825900 -0.771118529
## solo_KillDeathRatio.mtrx 1.0000000 -0.634358921
## solo_RoundsPlayed.mtrx -0.6343589 1.000000000
## solo_MoveDistancePg.mtrx 0.3529028 -0.333226265
## solo_DamagePg.mtrx 0.9722485 -0.560207655
## solo_KillsPg.mtrx 0.9859195 -0.576510743
## solo_AvgSurvivalTime.mtrx 0.4258529 -0.455848539
## solo_MoveDistancePg.mtrx solo_DamagePg.mtrx
## tracktrans -0.1402012 -0.1379252
## solo_rating.mtrx 0.1088186 -0.1643466
## solo_WinRatio.mtrx 0.4806081 0.7108651
## solo_KillDeathRatio.mtrx 0.3529028 0.9722485
## solo_RoundsPlayed.mtrx -0.3332263 -0.5602077
## solo_MoveDistancePg.mtrx 1.0000000 0.3467629
## solo_DamagePg.mtrx 0.3467629 1.0000000
## solo_KillsPg.mtrx 0.3158699 0.9733448
## solo_AvgSurvivalTime.mtrx 0.6657312 0.3979725
## solo_KillsPg.mtrx solo_AvgSurvivalTime.mtrx
## tracktrans -0.1345913 -0.09885554
## solo_rating.mtrx -0.1822523 -0.04991211
## solo_WinRatio.mtrx 0.7298163 0.54175661
## solo_KillDeathRatio.mtrx 0.9859195 0.42585294
## solo_RoundsPlayed.mtrx -0.5765107 -0.45584854
## solo_MoveDistancePg.mtrx 0.3158699 0.66573118
## solo_DamagePg.mtrx 0.9733448 0.39797252
## solo_KillsPg.mtrx 1.0000000 0.37297388
## solo_AvgSurvivalTime.mtrx 0.3729739 1.00000000
curvilinear relationship between Win Ratio and KDR, solo_rating and Rounds Played. Clear patterns hard to distinquish via visual analysis alone. Further plotting and statistical analysis is required. # Scatter plot of solo_rating vs each transformed variable 
# MoveDistancePg has an odd shape due to the nature of the game. As some players will often die from the very ofset of the game in a Hunger Games-esque battle arena. # Normal Q-Q plots of the transformed data 
## Warning in data.row.names(row.names, rowsi, i): some row.names duplicated:
## 2,3,4,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,38,39,40,41,42
## --> row.names NOT used## size Cp 1 2 3 4 5 6 SSEp AIC
## 37 6 8.315854 TRUE FALSE TRUE TRUE TRUE TRUE 62.43278 -32716.38
## SBC
## 37 -32675.3SBC criterion suggests that we disclude Log.solo_KillDeathRatio.nrm but retain the remaining predictors
## Warning: package 'corrplot' was built under R version 3.4.2## corrplot 0.84 loaded## solo_rating.mtrx solo_WinRatio.mtrx
## solo_rating.mtrx 1.00 -0.33
## solo_WinRatio.mtrx -0.33 1.00
## solo_KillDeathRatio.mtrx -0.22 0.78
## solo_RoundsPlayed.mtrx 0.69 -0.77
## solo_MoveDistancePg.mtrx 0.11 0.48
## solo_DamagePg.mtrx -0.16 0.71
## solo_KillsPg.mtrx -0.18 0.73
## solo_AvgSurvivalTime.mtrx -0.05 0.54
## solo_KillDeathRatio.mtrx solo_RoundsPlayed.mtrx
## solo_rating.mtrx -0.22 0.69
## solo_WinRatio.mtrx 0.78 -0.77
## solo_KillDeathRatio.mtrx 1.00 -0.63
## solo_RoundsPlayed.mtrx -0.63 1.00
## solo_MoveDistancePg.mtrx 0.35 -0.33
## solo_DamagePg.mtrx 0.97 -0.56
## solo_KillsPg.mtrx 0.99 -0.58
## solo_AvgSurvivalTime.mtrx 0.43 -0.46
## solo_MoveDistancePg.mtrx solo_DamagePg.mtrx
## solo_rating.mtrx 0.11 -0.16
## solo_WinRatio.mtrx 0.48 0.71
## solo_KillDeathRatio.mtrx 0.35 0.97
## solo_RoundsPlayed.mtrx -0.33 -0.56
## solo_MoveDistancePg.mtrx 1.00 0.35
## solo_DamagePg.mtrx 0.35 1.00
## solo_KillsPg.mtrx 0.32 0.97
## solo_AvgSurvivalTime.mtrx 0.67 0.40
## solo_KillsPg.mtrx solo_AvgSurvivalTime.mtrx
## solo_rating.mtrx -0.18 -0.05
## solo_WinRatio.mtrx 0.73 0.54
## solo_KillDeathRatio.mtrx 0.99 0.43
## solo_RoundsPlayed.mtrx -0.58 -0.46
## solo_MoveDistancePg.mtrx 0.32 0.67
## solo_DamagePg.mtrx 0.97 0.40
## solo_KillsPg.mtrx 1.00 0.37
## solo_AvgSurvivalTime.mtrx 0.37 1.00
##
## Call:
## lm(formula = solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_KillDeathRatio.nrm +
## Log.solo_RoundsPlayed.nrm + Sqrt.solo_MoveDistancePg.nrm +
## Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49385 -0.05885 -0.00151 0.06497 0.30345
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.888112 0.017449 50.898 <2e-16 ***
## Log.solo_WinRatio.nrm 0.029981 0.002299 13.043 <2e-16 ***
## Log.solo_KillDeathRatio.nrm 0.027397 0.015045 1.821 0.0687 .
## Log.solo_RoundsPlayed.nrm 0.154017 0.001595 96.546 <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm 0.451722 0.017285 26.134 <2e-16 ***
## Log.solo_KillsPg.nrm 0.031619 0.015844 1.996 0.0460 *
## solo_AvgSurvivalTime.nrm 0.135766 0.013817 9.826 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09483 on 6939 degrees of freedom
## Multiple R-squared: 0.6691, Adjusted R-squared: 0.6688
## F-statistic: 2338 on 6 and 6939 DF, p-value: < 2.2e-16There appears to be a strong correlation between solo_rating and RoundsPlayed, KillDeathRatio and WinRatio,etc. With a strong negative correlation between WinRatio and RoundsPlayed, which makes complete sense give one of the two is a ratio between games won vs games played.The correlation between MoveDistance and SurvivalTime is expected as well, as not only are the players going to be alive if they are moving around, as the game progresses, the remaining players are forced ever closer together.
## Warning: package 'MASS' was built under R version 3.4.3
## Start: AIC=-36299.62
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_RoundsPlayed.nrm +
## Sqrt.solo_MoveDistancePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm
##
## Df Sum of Sq RSS AIC
## <none> 37.271 -36300
## - solo_AvgSurvivalTime.nrm 1 0.573 37.844 -36196
## - Log.solo_WinRatio.nrm 1 0.738 38.009 -36165
## - Log.solo_KillsPg.nrm 1 2.209 39.480 -35902
## - Sqrt.solo_MoveDistancePg.nrm 1 4.001 41.272 -35593
## - Log.solo_RoundsPlayed.nrm 1 55.307 92.578 -29982
##
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm + Log.solo_RoundsPlayed.nrm +
## Sqrt.solo_MoveDistancePg.nrm + Log.solo_KillsPg.nrm + solo_AvgSurvivalTime.nrm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49111 -0.04401 0.00321 0.05227 0.19546
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.990952 0.011267 87.95 <2e-16 ***
## Log.solo_WinRatio.nrm 0.019820 0.001691 11.72 <2e-16 ***
## Log.solo_RoundsPlayed.nrm 0.122650 0.001209 101.48 <2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm 0.364488 0.013354 27.30 <2e-16 ***
## Log.solo_KillsPg.nrm 0.053757 0.002650 20.28 <2e-16 ***
## solo_AvgSurvivalTime.nrm 0.108895 0.010543 10.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07328 on 6940 degrees of freedom
## Multiple R-squared: 0.6903, Adjusted R-squared: 0.6901
## F-statistic: 3094 on 5 and 6940 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c +
## Log.solo_RoundsPlayed.nrm.c + Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c +
## Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c +
## Win.Rounds + Win.Kills + Win.Damage + Win.Move + Win.Time +
## Rounds.Kills + Rounds.Damage + Rounds.Move + Rounds.Time +
## Kills.Damage + Kills.Move + Kills.Time + Damage.Move + Damage.Time +
## Time.Move)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.46030 -0.04372 0.00304 0.05016 0.31231
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6509609 0.0013419 485.110 < 2e-16 ***
## Log.solo_WinRatio.nrm.c 0.0202971 0.0017370 11.685 < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c 0.1207529 0.0013213 91.391 < 2e-16 ***
## Log.solo_KillsPg.nrm.c -0.0010354 0.0129973 -0.080 0.936510
## Sqrt.solo_DamagePg.nrm.c 0.3419275 0.0812903 4.206 2.63e-05 ***
## Sqrt.solo_MoveDistancePg.nrm.c 0.3985045 0.0138355 28.803 < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c 0.1127655 0.0105687 10.670 < 2e-16 ***
## Win.Rounds 0.0006582 0.0011383 0.578 0.563111
## Win.Kills -0.0121923 0.0127992 -0.953 0.340833
## Win.Damage 0.1819949 0.0765381 2.378 0.017442 *
## Win.Move -0.0662632 0.0186590 -3.551 0.000386 ***
## Win.Time -0.1178422 0.0890083 -1.324 0.185565
## Rounds.Kills 0.0013214 0.0113609 0.116 0.907408
## Rounds.Damage -0.0445192 0.0631911 -0.705 0.481135
## Rounds.Move -0.0058920 0.0142294 -0.414 0.678834
## Rounds.Time 0.0024845 0.0103755 0.239 0.810759
## Kills.Damage -0.3353641 0.0313815 -10.687 < 2e-16 ***
## Kills.Move -0.2814325 0.1066222 -2.640 0.008321 **
## Kills.Time NA NA NA NA
## Damage.Move 1.0027123 0.5846875 1.715 0.086398 .
## Damage.Time 0.5826874 0.4987769 1.168 0.242753
## Time.Move -0.3919282 0.0965290 -4.060 4.96e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07149 on 6925 degrees of freedom
## Multiple R-squared: 0.7059, Adjusted R-squared: 0.7051
## F-statistic: 831.1 on 20 and 6925 DF, p-value: < 2.2e-16## Start: AIC=-36628.18
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move +
## Rounds.Time + Kills.Damage + Kills.Move + Kills.Time + Damage.Move +
## Damage.Time + Time.Move
##
##
## Step: AIC=-36628.18
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Log.solo_KillsPg.nrm.c + Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move +
## Rounds.Time + Kills.Damage + Kills.Move + Damage.Move + Damage.Time +
## Time.Move
##
## Df Sum of Sq RSS AIC
## - Log.solo_KillsPg.nrm.c 1 0.000 35.396 -36630
## - Rounds.Kills 1 0.000 35.396 -36630
## - Rounds.Time 1 0.000 35.396 -36630
## - Rounds.Move 1 0.001 35.397 -36630
## - Win.Rounds 1 0.002 35.398 -36630
## - Rounds.Damage 1 0.003 35.399 -36630
## - Win.Kills 1 0.005 35.401 -36629
## - Damage.Time 1 0.007 35.403 -36629
## - Win.Time 1 0.009 35.405 -36628
## <none> 35.396 -36628
## - Damage.Move 1 0.015 35.411 -36627
## - Win.Damage 1 0.029 35.425 -36625
## - Kills.Move 1 0.036 35.432 -36623
## - Win.Move 1 0.064 35.460 -36618
## - Time.Move 1 0.084 35.480 -36614
## - Sqrt.solo_DamagePg.nrm.c 1 0.090 35.486 -36612
## - solo_AvgSurvivalTime.nrm.c 1 0.582 35.978 -36517
## - Kills.Damage 1 0.584 35.980 -36517
## - Log.solo_WinRatio.nrm.c 1 0.698 36.094 -36495
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.240 39.636 -35844
## - Log.solo_RoundsPlayed.nrm.c 1 42.692 78.088 -31134
##
## Step: AIC=-36630.17
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Kills + Rounds.Damage + Rounds.Move +
## Rounds.Time + Kills.Damage + Kills.Move + Damage.Move + Damage.Time +
## Time.Move
##
## Df Sum of Sq RSS AIC
## - Rounds.Kills 1 0.000 35.396 -36632
## - Rounds.Time 1 0.000 35.396 -36632
## - Rounds.Move 1 0.001 35.397 -36632
## - Win.Rounds 1 0.002 35.398 -36632
## - Rounds.Damage 1 0.003 35.399 -36632
## - Win.Kills 1 0.005 35.401 -36631
## - Damage.Time 1 0.007 35.403 -36631
## - Win.Time 1 0.009 35.405 -36630
## <none> 35.396 -36630
## - Damage.Move 1 0.015 35.411 -36629
## + Log.solo_KillsPg.nrm.c 1 0.000 35.396 -36628
## - Win.Damage 1 0.029 35.425 -36627
## - Kills.Move 1 0.036 35.432 -36625
## - Win.Move 1 0.065 35.461 -36619
## - Time.Move 1 0.084 35.480 -36616
## - solo_AvgSurvivalTime.nrm.c 1 0.582 35.978 -36519
## - Log.solo_WinRatio.nrm.c 1 0.708 36.104 -36495
## - Kills.Damage 1 0.728 36.124 -36491
## - Sqrt.solo_DamagePg.nrm.c 1 1.636 37.032 -36318
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.369 39.765 -35824
## - Log.solo_RoundsPlayed.nrm.c 1 43.311 78.707 -31081
##
## Step: AIC=-36632.15
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Damage + Rounds.Move + Rounds.Time +
## Kills.Damage + Kills.Move + Damage.Move + Damage.Time + Time.Move
##
## Df Sum of Sq RSS AIC
## - Rounds.Time 1 0.000 35.396 -36634
## - Rounds.Move 1 0.001 35.397 -36634
## - Win.Rounds 1 0.002 35.398 -36634
## - Damage.Time 1 0.008 35.404 -36633
## - Win.Time 1 0.010 35.406 -36632
## <none> 35.396 -36632
## - Win.Kills 1 0.014 35.411 -36631
## - Damage.Move 1 0.015 35.411 -36631
## + Rounds.Kills 1 0.000 35.396 -36630
## + Log.solo_KillsPg.nrm.c 1 0.000 35.396 -36630
## - Rounds.Damage 1 0.029 35.425 -36628
## - Kills.Move 1 0.036 35.432 -36627
## - Win.Damage 1 0.063 35.459 -36622
## - Win.Move 1 0.065 35.461 -36621
## - Time.Move 1 0.084 35.481 -36618
## - solo_AvgSurvivalTime.nrm.c 1 0.583 35.979 -36521
## - Log.solo_WinRatio.nrm.c 1 0.709 36.105 -36496
## - Kills.Damage 1 0.728 36.124 -36493
## - Sqrt.solo_DamagePg.nrm.c 1 1.649 37.045 -36318
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.370 39.766 -35826
## - Log.solo_RoundsPlayed.nrm.c 1 43.548 78.944 -31062
##
## Step: AIC=-36634.1
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Damage + Rounds.Move + Kills.Damage +
## Kills.Move + Damage.Move + Damage.Time + Time.Move
##
## Df Sum of Sq RSS AIC
## - Rounds.Move 1 0.001 35.397 -36636
## - Win.Rounds 1 0.003 35.399 -36636
## - Damage.Time 1 0.008 35.404 -36635
## <none> 35.396 -36634
## - Win.Time 1 0.011 35.407 -36634
## - Win.Kills 1 0.014 35.411 -36633
## - Damage.Move 1 0.015 35.412 -36633
## + Rounds.Time 1 0.000 35.396 -36632
## + Rounds.Kills 1 0.000 35.396 -36632
## + Log.solo_KillsPg.nrm.c 1 0.000 35.396 -36632
## - Rounds.Damage 1 0.029 35.426 -36630
## - Kills.Move 1 0.035 35.432 -36629
## - Win.Damage 1 0.063 35.460 -36624
## - Win.Move 1 0.065 35.461 -36623
## - Time.Move 1 0.088 35.484 -36619
## - solo_AvgSurvivalTime.nrm.c 1 0.583 35.979 -36523
## - Log.solo_WinRatio.nrm.c 1 0.709 36.105 -36498
## - Kills.Damage 1 0.728 36.125 -36495
## - Sqrt.solo_DamagePg.nrm.c 1 1.651 37.047 -36319
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.372 39.768 -35827
## - Log.solo_RoundsPlayed.nrm.c 1 43.742 79.138 -31047
##
## Step: AIC=-36635.97
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Rounds + Win.Kills + Win.Damage +
## Win.Move + Win.Time + Rounds.Damage + Kills.Damage + Kills.Move +
## Damage.Move + Damage.Time + Time.Move
##
## Df Sum of Sq RSS AIC
## - Win.Rounds 1 0.002 35.399 -36638
## - Damage.Time 1 0.008 35.405 -36636
## <none> 35.397 -36636
## - Win.Time 1 0.011 35.408 -36636
## - Win.Kills 1 0.014 35.411 -36635
## - Damage.Move 1 0.016 35.413 -36635
## + Rounds.Move 1 0.001 35.396 -36634
## + Rounds.Kills 1 0.000 35.397 -36634
## + Log.solo_KillsPg.nrm.c 1 0.000 35.397 -36634
## + Rounds.Time 1 0.000 35.397 -36634
## - Rounds.Damage 1 0.032 35.429 -36632
## - Kills.Move 1 0.036 35.433 -36631
## - Win.Damage 1 0.063 35.460 -36626
## - Win.Move 1 0.079 35.476 -36623
## - Time.Move 1 0.088 35.485 -36621
## - solo_AvgSurvivalTime.nrm.c 1 0.585 35.982 -36524
## - Log.solo_WinRatio.nrm.c 1 0.714 36.111 -36499
## - Kills.Damage 1 0.730 36.127 -36496
## - Sqrt.solo_DamagePg.nrm.c 1 1.664 37.061 -36319
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.372 39.769 -35829
## - Log.solo_RoundsPlayed.nrm.c 1 43.875 79.272 -31038
##
## Step: AIC=-36637.52
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move +
## Win.Time + Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move +
## Damage.Time + Time.Move
##
## Df Sum of Sq RSS AIC
## - Damage.Time 1 0.008 35.407 -36638
## <none> 35.399 -36638
## - Win.Time 1 0.011 35.411 -36637
## - Damage.Move 1 0.015 35.415 -36637
## - Win.Kills 1 0.017 35.416 -36636
## + Win.Rounds 1 0.002 35.397 -36636
## + Rounds.Time 1 0.001 35.399 -36636
## + Rounds.Kills 1 0.000 35.399 -36636
## + Rounds.Move 1 0.000 35.399 -36636
## + Log.solo_KillsPg.nrm.c 1 0.000 35.399 -36636
## - Rounds.Damage 1 0.031 35.430 -36634
## - Kills.Move 1 0.034 35.434 -36633
## - Win.Damage 1 0.064 35.463 -36627
## - Time.Move 1 0.087 35.487 -36622
## - Win.Move 1 0.099 35.498 -36620
## - solo_AvgSurvivalTime.nrm.c 1 0.583 35.983 -36526
## - Log.solo_WinRatio.nrm.c 1 0.712 36.111 -36501
## - Kills.Damage 1 0.736 36.136 -36496
## - Sqrt.solo_DamagePg.nrm.c 1 1.750 37.149 -36304
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.532 39.932 -35803
## - Log.solo_RoundsPlayed.nrm.c 1 49.083 84.483 -30598
##
## Step: AIC=-36637.93
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move +
## Win.Time + Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move +
## Time.Move
##
## Df Sum of Sq RSS AIC
## - Win.Time 1 0.006 35.413 -36639
## <none> 35.407 -36638
## + Damage.Time 1 0.008 35.399 -36638
## + Win.Rounds 1 0.003 35.405 -36636
## + Rounds.Kills 1 0.001 35.406 -36636
## + Rounds.Time 1 0.001 35.407 -36636
## + Rounds.Move 1 0.000 35.407 -36636
## + Log.solo_KillsPg.nrm.c 1 0.000 35.407 -36636
## - Rounds.Damage 1 0.037 35.444 -36633
## - Win.Kills 1 0.038 35.445 -36632
## - Damage.Move 1 0.040 35.447 -36632
## - Kills.Move 1 0.069 35.477 -36626
## - Time.Move 1 0.082 35.490 -36624
## - Win.Damage 1 0.102 35.510 -36620
## - Win.Move 1 0.104 35.511 -36620
## - solo_AvgSurvivalTime.nrm.c 1 0.583 35.991 -36526
## - Log.solo_WinRatio.nrm.c 1 0.715 36.122 -36501
## - Kills.Damage 1 0.743 36.150 -36496
## - Sqrt.solo_DamagePg.nrm.c 1 1.742 37.150 -36306
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.527 39.935 -35804
## - Log.solo_RoundsPlayed.nrm.c 1 49.150 84.557 -30593
##
## Step: AIC=-36638.79
## Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move +
## Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move +
## Time.Move
##
## Df Sum of Sq RSS AIC
## <none> 35.413 -36639
## + Win.Time 1 0.006 35.407 -36638
## + Kills.Time 1 0.006 35.407 -36638
## + Rounds.Time 1 0.003 35.410 -36637
## + Win.Rounds 1 0.003 35.410 -36637
## + Damage.Time 1 0.003 35.411 -36637
## + Rounds.Kills 1 0.001 35.412 -36637
## + Log.solo_KillsPg.nrm.c 1 0.000 35.413 -36637
## + Rounds.Move 1 0.000 35.413 -36637
## - Rounds.Damage 1 0.033 35.446 -36634
## - Win.Kills 1 0.036 35.449 -36634
## - Damage.Move 1 0.043 35.456 -36632
## - Kills.Move 1 0.083 35.496 -36625
## - Win.Damage 1 0.097 35.511 -36622
## - Time.Move 1 0.099 35.512 -36621
## - Win.Move 1 0.100 35.513 -36621
## - solo_AvgSurvivalTime.nrm.c 1 0.578 35.991 -36528
## - Log.solo_WinRatio.nrm.c 1 0.710 36.123 -36503
## - Kills.Damage 1 0.737 36.151 -36498
## - Sqrt.solo_DamagePg.nrm.c 1 1.768 37.182 -36302
## - Sqrt.solo_MoveDistancePg.nrm.c 1 4.580 39.994 -35796
## - Log.solo_RoundsPlayed.nrm.c 1 49.151 84.564 -30595The most significant interaction effects are WinRatio to MoveDistance, KillsPg to DamagePg, SurvivalTime To MoveDistance. The only significant relationship that isn’t immediately obvious as to why the P-value is so significant is WinRatio to MoveDistance. With Kills Pg to DamagePg, given enough damage, a character will ‘die’ and that player is out of the competition for first place, meaning that if a person has a large value in Kills per game, they must have a large value in damage per game. But it looks like there is a strong correlation between Win ratio and Move Distance per game, meaing that those players that are able to survive and move around are much more likely to win more and get a better rating.
##
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c +
## Log.solo_RoundsPlayed.nrm.c + Sqrt.solo_DamagePg.nrm.c +
## Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c +
## Win.Kills + Win.Damage + Win.Move + Rounds.Damage + Kills.Damage +
## Kills.Move + Damage.Move + Time.Move)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45823 -0.04345 0.00304 0.05031 0.29843
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.650697 0.001165 558.417 < 2e-16 ***
## Log.solo_WinRatio.nrm.c 0.020085 0.001704 11.787 < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c 0.121051 0.001234 98.087 < 2e-16 ***
## Sqrt.solo_DamagePg.nrm.c 0.337547 0.018143 18.605 < 2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm.c 0.401127 0.013396 29.943 < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c 0.111336 0.010468 10.636 < 2e-16 ***
## Win.Kills -0.018297 0.006918 -2.645 0.00820 **
## Win.Damage 0.209453 0.047977 4.366 1.29e-05 ***
## Win.Move -0.065846 0.014909 -4.417 1.02e-05 ***
## Rounds.Damage -0.033661 0.013333 -2.525 0.01161 *
## Kills.Damage -0.329517 0.027429 -12.013 < 2e-16 ***
## Kills.Move -0.360068 0.089397 -4.028 5.69e-05 ***
## Damage.Move 1.426012 0.492683 2.894 0.00381 **
## Time.Move -0.404073 0.091906 -4.397 1.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07147 on 6932 degrees of freedom
## Multiple R-squared: 0.7058, Adjusted R-squared: 0.7052
## F-statistic: 1279 on 13 and 6932 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Model 1: Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move +
## Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move +
## Time.Move
## Model 2: Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c + Log.solo_RoundsPlayed.nrm.c +
## Sqrt.solo_DamagePg.nrm.c + Sqrt.solo_MoveDistancePg.nrm.c +
## solo_AvgSurvivalTime.nrm.c + Win.Kills + Win.Damage + Win.Move +
## Rounds.Damage + Kills.Damage + Kills.Move + Damage.Move +
## Time.Move
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 6932 35.413
## 2 6932 35.413 0 0Difference between models have a p-value of 0.
# All the plots for the reduced stepwise model look nice, with a few outliers, none outside the cook’s distance.There is one standardized residual that has an absolute value greater than 4.
## Warning in par(mfrom = c(1, 2)): "mfrom" is not a graphical parameter## Warning: package 'car' was built under R version 3.4.3
## [1] 0.08978972
## Log.solo_WinRatio.nrm.c Log.solo_RoundsPlayed.nrm.c
## 4.347732 2.764840
## Sqrt.solo_DamagePg.nrm.c Sqrt.solo_MoveDistancePg.nrm.c
## 3.109261 2.007873
## solo_AvgSurvivalTime.nrm.c Win.Kills
## 2.139084 27.018522
## Win.Damage Win.Move
## 47.445147 3.509912
## Rounds.Damage Kills.Damage
## 4.803084 5.582264
## Kills.Move Damage.Move
## 27.635295 30.185092
## Time.Move
## 2.119333## [1] 12.51288The variance inflation factors range from 2 to 47.45. The latter being for Win Ratio and Damage. The VIF is greater than 10 for Win.Kills, Win.Damage, Kills.Move, Damage.Move. With a mean of 12.51.
##
## Call:
## lm(formula = Sqrt.solo_Rating.nrm ~ Log.solo_WinRatio.nrm.c +
## Log.solo_RoundsPlayed.nrm.c + Sqrt.solo_DamagePg.nrm.c +
## Sqrt.solo_MoveDistancePg.nrm.c + solo_AvgSurvivalTime.nrm.c +
## Win.Kills + Win.Damage + Win.Move + Rounds.Damage + Kills.Damage +
## Kills.Move + Damage.Move + Time.Move)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45823 -0.04345 0.00304 0.05031 0.29843
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.650697 0.001165 558.417 < 2e-16 ***
## Log.solo_WinRatio.nrm.c 0.020085 0.001704 11.787 < 2e-16 ***
## Log.solo_RoundsPlayed.nrm.c 0.121051 0.001234 98.087 < 2e-16 ***
## Sqrt.solo_DamagePg.nrm.c 0.337547 0.018143 18.605 < 2e-16 ***
## Sqrt.solo_MoveDistancePg.nrm.c 0.401127 0.013396 29.943 < 2e-16 ***
## solo_AvgSurvivalTime.nrm.c 0.111336 0.010468 10.636 < 2e-16 ***
## Win.Kills -0.018297 0.006918 -2.645 0.00820 **
## Win.Damage 0.209453 0.047977 4.366 1.29e-05 ***
## Win.Move -0.065846 0.014909 -4.417 1.02e-05 ***
## Rounds.Damage -0.033661 0.013333 -2.525 0.01161 *
## Kills.Damage -0.329517 0.027429 -12.013 < 2e-16 ***
## Kills.Move -0.360068 0.089397 -4.028 5.69e-05 ***
## Damage.Move 1.426012 0.492683 2.894 0.00381 **
## Time.Move -0.404073 0.091906 -4.397 1.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07147 on 6932 degrees of freedom
## Multiple R-squared: 0.7058, Adjusted R-squared: 0.7052
## F-statistic: 1279 on 13 and 6932 DF, p-value: < 2.2e-16From this final model we can see the effect that each predictor has on increasing our response variable solo rating. The predictor with the largest estimate is solo_moveDistancePg, and solo_DamagePg. Meaing that if a player wants to increase their solo rating in PUBG they should move around the arena a lot in search of more gear and more enemies to fight. Since KillsPg and DamagePg are so highly correlated, the removal of one of those predictors does not harm the model greatly. Although survival is the ultimate goal of every PUBG game, this does not mean that a player should sit tight and wait until the rest of the players fight each other. To get a better rating most effectively, a player should work on effectivley manuvering the arena and become proficint in player to player combat.